To find the area of Crystal's scale drawing of the triangle, we first need to calculate the area of the original triangle.
The formula for the area of a triangle is:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
For the original triangle:
- Base = 8 inches
- Height = 5 inches
Substituting these values into the formula:
\[ \text{Area} = \frac{1}{2} \times 8 \times 5 = \frac{1}{2} \times 40 = 20 \text{ square inches} \]
Next, we need to determine the area of the scale drawing. The height of the scale drawing is 2 inches, and the original height is 5 inches, indicating a scaling factor. The scale factor can be found by comparing the heights:
\[ \text{Scale factor} = \frac{\text{height of scale drawing}}{\text{height of original triangle}} = \frac{2}{5} \]
Since the area scales with the square of the linear dimensions, the area of the scale drawing can be calculated using the square of the scale factor:
\[ \text{Area of scale drawing} = \text{Area of original triangle} \times \left(\text{Scale factor}\right)^2 \]
Calculating the area of the scale drawing:
\[ \text{Area of scale drawing} = 20 \times \left(\frac{2}{5}\right)^2 = 20 \times \frac{4}{25} = 20 \times 0.16 = 3.2 \text{ square inches} \]
Therefore, the area of Crystal's scale drawing is 3.2 square inches.
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